Question

Two students are selected to represent AMCHS at the Senate meeting. If there are 5 athletes, 7 band members, and 3 student council members, what is the probability that the 2 representatives will both be athletes?

Answer 1

the probability- 5/15

Answer 2

To find the probability that both representatives will be athletes, you can use the concept of conditional probability. You first find the probability of the first representative being an athlete and then, assuming the first representative is an athlete, find the probability that the second representative is also an athlete.

There are 5 athletes out of a total of 5 + 7 + 3 = 15 students eligible to be representatives.

So, for the first representative to be an athlete, the probability is 5/15.

Now, if the first representative is an athlete, there are 4 athletes left out of the remaining 14 students.

So, the probability that the second representative is also an athlete, given that the first one is, is 4/14.

To find the overall probability of both representatives being athletes, you multiply these probabilities:

(5/15) * (4/14) = (1/3) * (2/7) = 2/21

So, the probability that both representatives will be athletes is 2/21.

Explanation: